; Date: Thu, 06 Oct 2011 22:50:25 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 06-10-11 (A Seahorse Goes East [7]) ; Id: <1.5.4.16.20111006225017.11e7b7ee@pop.earthlink.net> ; --------- ; ; FOTD -- October 06, 2011 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; In today's FOTD we see the scene I was searching for yesterday ; when the fractal ship showed up. I named the image "A Seahorse ; Goes East" because it combines the features of Seahorse Valley ; with those of East Valley. ; ; The outer parts of the scene are clearly of an East Valley ; nature, while the inner parts reflect the appearance of Seahorse ; Valley when sliced in the Oblate direction, which is determined ; by the imag(c) and real(z) axes. The entire image is distorted ; into a vague triangular shape because it lies at an odd angle in ; the 4-D Julibrot figure. ; ; (As a matter of curiosity, in the German language, the word ; 'julibrot' means 'bread of July'.) ; ; Unlike yesterday's image, which was stretched and skewed beyond ; verbal description, today's image was stretched only a modest ; 3-1/2 times in the horizontal direction. The value assigned the ; real(p4) parameter, which sets real(z) is equal to the real(c) ; value of the scene in the M-set. This places the actual ; location of the scene in what I call the shadow Mandelbrot set, ; a second Mandelbrot set lurking unsuspected at an angle of 45,45 ; degrees in the Z^2+C Julibrot. ; ; The rating of a 7 is an improvement over yesterday's miserable ; rating of 4, but still leaves plenty room for yet more ; improvement. The calculation time of a mere 24 seconds will ; make running the parameter file a breeze. The task of setting ; up and running the file may be avoided by viewing the image on ; the web site. ; ; The finished image should soon be posted on the official FOTD ; web site at: ; ; ; ; I said 'should be posted' because the last time I checked, the ; site was refusing access due to a hack attack. ; ; The image is also posted at: ; ; ; ; in high definition. ; ; The original web site may be accessed at: ; ; ; ; Strange as it might seem, as the number of hypercube dimensions ; increases, its diagonal approaches infinity, while the ; hypervolume of the inscribed hypersphere approaches zero percent ; of that of the hypercube. ; ; BTW, the formula for the hypervolume of a six-dimensional ; hypersphere is 1/6(pi^3)*(r^6). ; ; Not a single cloud spoiled the blueness of the sky over Fractal ; Central today. The sunrise temperature of 36F +2C was rather ; chilly, but the unbroken sunshine brought the afternoon tempera- ; ture to a pleasant 66F 19C, while the near calm winds made the ; day as close to ideal as we have had in two months. And the ; best part is that the near perfect conditions are expected to ; prevail for a week. ; ; The fractal cats, always seeking perfection, found it on their ; shelf in the sunny southwest window. The humans, realizing that ; perfection never happens, took the day for what it had to offer. ; The next FOTD will be posted in 24 hours. Until then, take ; care, and I agree with the angry young protesters. We should ; abolish poverty. But does anyone know how we might bring about ; this utopian dream? ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= A_SeahorseGoesEast { ; time=0:00:24.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/\ +0.0000003835126177/419409.6/3.4337 params=0/90/0/90/-1.747855067330428/0/-1.747855067\ 330428/0 float=y maxiter=32767 inside=255 logmap=99 symmetry=yaxis periodicity=6 colors=00010S20U30W40Y50_60a70c80e90gA0iA0kA1lC2mE\ 3nH4oJ4pH4oE4mB4j84g84c84_84W75S75P75L64U53c42m3Lu\ cOzclLhsHmzDrz9wzBzzBzzzO7LNAQLDVKG_IJdHMiJQjKTjLW\ jM_jNbjOejPijQljRojSsjTvjUyjXrl_knadpdYr_qNYjPWcSU\ XUSQWQJZOC`oC1E3WM5bU6ia8pi9waJrVTnNajGkf6x_9tbBqe\ DnhFkkHhnLZpJeqHkqFrqExqPng_eZjXQjYOjYMjYKjYJjYHjY\ FxR5qVAjYEsfQkcMc`IWYEOVAGS61dv5XU8Q2FP6LO9SNCYMFd\ LIjKLaOOUSQLWS7aWA`VD_UF_TIZSLYRHfIKaMNYQKZaPWaTTa\ YQaaNa`Q_dXfibmmhsrnzpzzvtzowzpqzmttjopgjodgqaekZb\ iW`gTZeP`gQXdRTbSQ`TMYUJWVFUVCS_HLcDGg9Bk56n12k54i\ 95fD7dH8bLA_PBYTDVXET`GRdHJWFCNE5ED0T`1XY1_V1bT1eQ\ 1hO5kLAnJFqGKtEPwBUz9Zx8cwAhv7mu7mt7ms6mr6oq5qp5so\ 5un4wm4xl4zk5zk5zk6zj6vj6rj7mi7mi7mi8mh8mh9mh9mg9m\ gAmgAmgAmc8m_7mW6mS5mP4mL3lH2rD1xA0eBDOCQ6CaDKaKRa\ RYaYdadkajraksdltfmuhnvjowlpxnqyprzjszdtz_uzXvz_wz\ bxzeyzhzzkzznzzqzztzzw000 } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;